Wednesday, January 16, 2013

Wittgenstein, Determinism, and Probability

One of the oldest philosophical questions is whether the Universe is deterministic or indeterministic. In a strictly deterministic universe everything that happens unfolds, causally, from the previous configuration of the universe. In such a universe, the thinking typically goes, man has no Free Will. We do what we are compelled to do by the rules of the Universe, or by the gods, if you prefer religious terminology. Our lives are controlled by Fate.

The advent of quantum physics threw a monkey wrench into the deterministic view of the universe constructed by scientists between 1600 and 1900. After considerable debate and experimentation, quantum physicists decided that at least some things in the universe happened by chance. This gave strength to the Free Will schools of philosophy and religion.

As far as I know my favorite philosopher, Ludwig Wittgenstein, did not decree the universe to be deterministic, or indeterministic either. Wittgenstein was a philosopher's philosopher. He offered no direct guidance to living life, unlike say Friedrich Nietzsche or Henry David Thoreau. In fact it is hard to find a place where he said anything definite about the universe, at least not after his earliest work, the Tractatus Logico-Philosophicus.

In his later works, including Philosophical Investigations, you might say that Wittgenstein deconstructs philosophy. But he is not a nihilist. For Wittgenstein the universe exists, it is no illusion. Instead what gives the aura of illusion to much philosophy, religion, and magical thinking is a swarm of errors that result from careless reasoning and the inexact nature of English and the other languages we use to do our thinking.

So what can best be learned from Wittgenstein is a technique, a critical attitude. It is similar to the ancient Socratic method of asking questions that lead a student to a correct, if complex, viewpoint. The trick to the Socratic method is asking the correct questions. I've never seen a formula for generating the correct questions. Wittgenstein provides no explicit formula, but his later works provide large numbers of examples of trying to apply an analytic (but often intuitive) process to philosophy itself. Frequently we are led to conclude that philosophy, like religion, is riddled with nonsense. Eliminating nonsense is one Herculean task that must be done if you want a clean stable for your ideas about the world.

Based on looking at many human and natural phenomena, we don't need to abandon the terms deterministic and indeterministic. What we have to do is use them more carefully and to realize that in certain situations there are shades of gray between them, and even room for both to be present in the same phenomena.

One of the most interesting and well-examined domains is probabilistic phenomena. We can speak of the probabilities of drawing an inside straight in poker, of an atom of radium decaying within the next pico second, of fog in the morning in London in February, or of Aunt Betty calling unexpectedly. But probability is another big word that may be misleading if we over generalize. Does shuffling a deck of cards create the same sort of probability as weather or quantum uncertainty?

Probability can exist in both a determinate world and an indeterminate world. From Newton's time until Heisenberg every throw of the dice was believed by scientists to be subject to the laws of (what we now call) classical physics, laws that were totally deterministic. Sure, with 2 dice, snake eyes came up every so often, and seven came up a reliable percentage of the time, but that was because humans had devised this method to introduce randomness. The dice were supposed to be shook up or thrown hard, making slight variations in muscle movements, too small to consciously control, result in outcomes that the thrower could not predict. A man of skill, throwing carefully, might cause dice to produce specified results at least some of the time, but other men monitored such cheating. The end result, fair or cheat, was determined by the placement of the dice in space, the momentum of the throw (including angular momentum), the exact characteristics of their bounces, and even the friction of the air.

When quantum physicists first discovered random atomic events many thought that there would prove to be underlying non-random, deterministic events that could explain the randomness. Much like Newtonian physics could explain, at least in theory, any particular throw of the dice. Einstein, for instance, believed that. But they were wrong, as far as anyone can tell. Many atomic and subatomic events do follow classical physics. Momentum, for instance, is preserved in atomic collisions. But decay processes, including radioactive decay and the emission of a light quanta by an electron "falling" from a high energy "orbit" to a lower energy orbit seem to be random events. At least within an envelope.

An envelope? They always leave that factoid out when religious gurus who specialize in the mechanics of separating their followers from money are elevating Quantum Physics to a Recipe for Mysticism. An envelope, here, is a metaphor for bounded probabilities. For instance, no matter how many times you role a pair of dice, the results are limited to the numbers between 2 and 12. That in itself is a kind of fuzzy determinism. Casinos, the old-fashioned kind with roulette wheels and people dealing cards, were built of fuzzy determinism. You could not predict which gamblers would win or lose any given hand or turn of the wheel, but at the end of the night the casino had more money than it started with.

Likewise a radioactive atom. You can't know when a particular atom will decay, but you can bet on a large group of atoms of the same element and not lose your shirt because the group emits radiation at a very predictable rate.

Once you start putting atoms together you quickly reach a point where quantum physics becomes pointless and you might as well fall back on classical physics. Yet engineers can build machines that make use of quantum mechanics for devices humans use, as shown by almost every electronic device made since the invention of the transistor. We use quantum uncertainty in our devices, yet we do that to increase predictable, deterministic behavior. If our devices get a glitch, the most likely sources are not quantum mechanical fluctuations outside the expected envelope but the failure of old classical components like a battery or solder joint.

So be careful about philosophical extrapolation. Or remember the modern key to all knowledge and wisdom: It's Complicated. You are made up of the same stuff of the rest of the universe, the arrangement is just different. We are arranged like mammals, only more so. Thinking about Free Will or Not Free Will will not help you make a decision. So take a deep breath and know that causality and randomness, determinism and indeterminism, are both going on all the time, within you and without you.

This essay is offered as a sacrifice to the Roman goddess Fortuna, and to the lucky Roman soldiers who won Jesus Christ's clothes at the crucifixion.